BASIC TRANSFORMATION


Animation are produced by moving the 'camera' or the objects in a scene along animation paths. Changes in orientation, size and shape are accomplished with geometric transformations that alter the coordinate descriptions of the objects. The basic geometric transformations are translation, rotation, and scaling. Other transformations that are often applied to objects include reflection and shear.

Use of transformations in CAD


In mathematics, "Transformation" is the elementary term used for a variety of operation such as rotation, translation, scaling, reflection, shearing etc. CAD is used throughout the engineering process from conceptual design and layout, through detailed engineering and analysis of components to definition of manufacturing methods. Every aspect of modeling in CAD is dependent on the transformation to view model from different directions we need to perform rotation operation. To move an object to a different location translation operation is done. Similarly Scaling operation is done to resize the object.

Coordinate Systems


In CAD three types of coordinate systems are needed in order to input, store and display model geometry and graphics. These are the Model Coordinate System (MCS), the World Coordinate System (WCS) and the Screen Coordinate System (SCS).

Model Coordinate System

 The MCS is defined as the reference space of the model with respect to which all the model geometrical data is stored. The origin of MCS can be arbitrary chosen by the user.

 

 

World Coordinate System

As discussed above every object have its own MCS relative to which its geometrical data is stored. Incase of multiple objects in the same working space then there is need of a World Coordinate System which relates each MCS to each other with respect to the orientation of the WCS. It can be seen by the picture shown below.

 

Screen Coordinate System

In contrast to the MCS and WCS the Screen Coordinate System is defined as a two dimensional device-dependent coordinate system whose origin is usually located at the lower left corner of the graphics display as shown in the picture below. A transformation operation from MCS coordinates to SCS coordinates is performed by the software before displaying the model views and graphics.

Viewing Transformations


As discussed that the objects are modeled in WCS, before these object descriptions can be projected  to the view plane, they must be transferred to viewing coordinate system. The view plane or the projection plane, is set up perpendicular to the viewing zv axis. The World coordinate positions in the scene are transformed to viewing  coordinates, then viewing coordinates are projected onto the view plane.

The transformation sequence to align WCS with Viewing Coordinate System is.

1. Translate the view reference point to the origin of the world coordinate system.

2. Apply rotations to align xv, yv, and zv with the world xw, yw and zw axes, respectively.